Details

sample66.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1651	48
done	5002	48

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.9b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.3b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 208

Calls

4 calls:

186.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
184.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
420.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
206.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
174.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
272.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify880.0ms

Counts

220 → 220

Iterations

Useful iterations: done (865.0ms)

Iter	Nodes	Cost
0	366	12421
1	1232	11265
done	5000	9611

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
4.5b	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
34.9b	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
39.7b	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
61×	`add-exp-log` `add-cbrt-cube`
57×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
29×	`cbrt-undiv` `div-exp`
15×	`div-inv`
14×	`associate-/r` `associate-/l`
13×	`difference-of-squares`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `associate-/l/`
2×	`associate-*r/` `fma-udef`
1×	`pow2` `distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 187

Calls

4 calls:

14.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
60.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
153.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
18.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
328.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.2s	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
197.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.3s

Counts

199 → 199

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	330	10445
1	909	9614
2	3975	8391
done	5001	7837

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
6.3b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
34.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite852.0ms

Algorithm

rewrite-expression-head

Rules

1905×	`times-frac`
1544×	`*-un-lft-identity`
1135×	`add-sqr-sqrt`
696×	`associate-r`
654×	`add-cube-cbrt`
396×	`distribute-lft-out`
392×	`sqrt-prod`
230×	`difference-of-squares`
115×	`distribute-lft-out--`
93×	`add-exp-log` `add-cbrt-cube`
44×	`cbrt-undiv` `div-exp`
39×	`div-inv`
26×	`prod-exp` `cbrt-unprod`
18×	`associate-/r/`
12×	`associate-l`
8×	`pow1`
5×	`frac-times` `associate-*l/` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`flip3--` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--`

Counts

4 → 819

Calls

4 calls:

649.0ms	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
46.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
2.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.9s

Counts

4 → 12

Calls

4 calls:

3.0s	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
678.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
77.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
118.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.3s

Counts

831 → 831

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	833	54880
1	2765	51762
done	5001	49603

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 33.3b

localize47.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (sqrt (+ (+ alpha beta) i)))
6.3b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
34.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite662.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
12×	`add-cube-cbrt` `associate-l` `sqrt-prod`
10×	`associate-/r/`
8×	`pow1` `cbrt-undiv` `div-exp` `associate-r` `prod-exp` `cbrt-unprod`
6×	`frac-times` `flip3-+` `times-frac` `flip-+`
5×	`associate-*l/`
4×	`expm1-log1p-u` `sqrt-div` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative`

Counts

4 → 106

Calls

4 calls:

195.0ms	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (sqrt (+ (+ alpha beta) i)))
453.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
4.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.9s

Counts

4 → 12

Calls

4 calls:

941.0ms	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (sqrt (+ (+ alpha beta) i)))
818.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
83.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
85.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	218	3955
1	580	3704
2	2220	3156
done	5001	3149

prune725.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 33.3b

regimes229.0ms

Accuracy

34% (2.6b remaining)

Error of 36.7b against oracle of 34.2b and baseline of 38.0b

bsearch52.0ms

Steps

Iters	Range		Point
4	1.5082760337526814e+194	2.4500393892790683e+194	1.5377061386128808e+194

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	70
1	30	70
done	30	70

end0.0ms

sample1.6s

Algorithm

intervals

Results

843.0ms	8000×	body	80	valid
364.0ms	8000×	pre	80	true